That's an excellent and very practical question for anyone living in a cold climate. I've wondered the same thing myself when taking out the trash on those brutally cold mornings. The short answer is: it depends, but most modern urban trash bins are designed to handle it.
The key factor is the type of plastic. Most municipal bins are made from high-density polyethylene (HDPE). This material is known for its good impact resistance even at low temperatures. It's designed to flex slightly rather than become immediately brittle. So, in normal winter conditions, a quality bin shouldn't just crack open if it's undisturbed.
However, there are limits. Extreme, sustained cold (think well below -20°F / -29°C) can make any plastic more brittle. The risk increases if the bin is already aged, UV-damaged from the sun, or has existing stress cracks. The real danger often comes from impact. A full, heavy bin that gets knocked over or hit by a plow on a frigid day is more likely to crack than one sitting still.
A few tips from experience: Try to avoid letting wet, heavy trash freeze solid to the bottom and sides, as prying it out can stress the plastic. If you can, store the bin in a slightly sheltered spot, like against the house, to reduce wind chill exposure. Also, be gentle when moving it in deep cold.
So, while it's not a guarantee, you can be reasonably confident. City planners and manufacturers specifically test for this. If you're truly concerned, you could look for bins labeled as "all-weather" or with a specified low-temperature tolerance. For most of us, though, the standard issue bin is a surprisingly resilient piece of urban engineering.